Spheroidal tank



y 3, 1967 K. M. CRAIG 3,320,994

SPHERO IDAL TANK Filed Dec. 29, 1965 2 Sheets-Sheet l 11v VENTOI? KE/VYO/V M. CRAIG m gpuafl By 5 TORNEY$ y 3 1967 K. M. C'RMG 3,320,994

SPHEROIDAL TANK Filed Dec. 29, 1965 2 Sheets-Sheet 2 STRESS(6) (PSI) 30 4000- 3000- H(FT.)

2000 I A=l2.6

A=IO.3 775 ELONGATION vowmmssu 30900 INVENTOI? KEN YON M. CRAIG BY 56 W TOR/VEYS United States Patent 3,320,994 SPHEROIDAL TANK Kenyon M. Craig, 51 Windermere Ave, Landsdowne, Pa. 19050 Filed Dec. 29, 1965, Ser. No. 517,211 Claims. (Cl. 150.5)

This invention relates to an improvement in large storage tanks of the type which are used for substantial quantities of fluids such as gases or liquid hydrocarbons. More specifically, this invention pertains to spheroidal tanks which have a particular configuration which permits the material of which they are formed to sustain uniform tensile forces throughout their extent. Also, the tanks are made of a stretchable, flexible material which permits them to expand in order to accommodate the capacity for which they are designed, and to assume their preferred shape.

The practice of this invention is related to large storage tanks which have a capacity in excess of 10,000 gallons of water; however, it is expected that those tanks having a capacity in excess of 50,000 gallons will provide the major utilization of the invention.

Heretofore, most large storage tanks have been vertically oriented cylindrical bodies. Due to the substantial depth of fluid in the larger of these tanks and/or the substantial diameter of the tank, it has been necessary to use thick walls in their lower portions in order to Withstand the usual fluid pressures. This, of course, reduces the stresses in the lower portions of the vertical tank Walls and thus precludes failure of the tank when it is filled to capacity.

Due to the substantial area of the liquids surface which is exposed to the atmosphere, either directly or by a vent, evaporation losses are considerable in most cylindrical tanks. Floating tops or covers will reduce evaporation losses, but these covers themselves are expensive to install and maintain.

Evaporation losses may be prevented by sealing the tank from the atmosphere, so that it is a substantially closed vessel with no avenues of escape for gaseous vapors. This, however, increases the internal pressure within the tank to a level which requires increased shell thickness. Economically, this has proven to be impractical.

One answer to the aforementioned problems has been the adoption of flat spheroidal tanks such as the ones disclosed in United States Patent 1,622,787 to George T. Horton. Basically, this is a rigid steel tank which is symmetrical about a vertical axis. Its bottom portion is flat and its sides and top, viewed in a plane through the axis of symmetry, is a curve the arcs of which have progressively decreasing radii from the top to the bottom of the tank.

The flat spheroidal tanks are shaped so that the differences in tensile forces in the tank shell are minimized. The vertical tensile forces in the shell at the top of the tank are ideally the same as those at the bottom of the tank when the tank is loaded to its design capacity. This enables a fabricator to use plates of uniform thickness in all portions of the tank. Of course, there is no evaporation loss since the tank is closed and its contents are maintained under pressure.

The flat spheriodal steel tanks have been of substantial commercial value, but they have some inherent disadvantages which are remedied by this invention. A foremost disadvantage is the difficulty in fabrication and installation. Like most tanks, these are built by fastening together a number of steel plates by riveting, welding or other conventional fastening means. Due to the complex curvatures of these tanks, the steel plates are not easily interchangeable, their fabrication tolerances are closed and the costs 3,320,994 Patented May 23, 196? of manufacture are high. Skilled crews familiar with these tanks must participate in their erection, which adds appreciably to the initial costs.

Like all ferrous tanks, the prior art spheroidal tanks require regular maintenance in the way of painting to protect them from the corrosive effects of the atmosphere. In large tan-k farms, this amounts to an expense which is obviated by the tanks of this invention.

Rigid spheroidal tanks are subjected to undesirable stresses as they are filled to varying degrees or with different types of fluids. For example, if a tank is designed to contain liquid and 10% gas having a pressure of 10 p.s.i., it will have vertical tensile forces in the material which are equal at all portions of the tank only when it is filled to the prescribed condition. If the pressure is reduced or the liquid level lowered, uneven forces will result which tend to bulge various portions of the shell. For this reason, the practical embodiments of these tanks must be designed with large safety factors and with additional bracing in the vulnerable areas.

Also, since the gas-to-liquid ratio is varying constantly, some compromise shape must be selected so that any deviation from the ideal loading condition will not cause failure of the tank.

In the prior art, it has been suggested that flattened, spheroidal tanks be made of a flexible fabric material. This obviates some of the problems of the substantially rigid spheriodal tanks, but there are deficiencies in these devices. As a practical matter, their strength cannot be as great as the strength of steel, so great care must be exercised to keep from overstressing the fabric shell. The nature of the fabric shell and the incompressibility of the liquid contents of the shell will cause the shell to burst when it is filled to an amount slightly in excess of its capacity.

The present invention overcomes the above-discussed shortcomings of the prior art in a most efficient and effective manner. Simply, the invention involves a flattened spheroidal tank which initially has a size smaller than its final size. The walls or shells are formed of a flexible material which is stretchable so that the tank may be expanded and, through all degrees of its expansion, it will assume a shape which approaches that ideal or basic shape which produces uniform tensile forces throughout the tank.

A primary object of this invention is to provide a fluid storage tank which is easily fabricated and erected, and which is, on the whole, appreciably more economical than tanks presently used for fluid storage. The economy of this tank results from a relatively low construction cost as contrasted to steel spheroidal tanks, low maintenance costs and the elimination of evaporation losses of stored liquids.

The reduction in fabrication and erection costs of the tank of this invention stems from the facts that (l) a relatively small area is required to initially construct the tank, due to its ability to expand when on a .site; (2) collapsibility of the tank renders it susceptible to convenient trans-portion to a site; and (3) erection involves simple preparation of a supporting surface, location of the tank thereon and filling of the tank, without complicated assembly procedures and extraneous bracing.

Another object of this invention is to provide a tank which makes the most efficient use of the materials from which it is constructed. This is because the tank contours conform to a basic shape equation defined below which results in equal tensile forces in all portions of the tank and because the shape of the tank adapts itself to changing loading conditions. This permits the use of material of uniform thickness for the entire tank.

Still another object is to provide a practically maintenance-free tank which requires no preservatives to prevent corrosion, and which can withstand exposure to the elements for an almost indefinite length of time.

A more complete understanding of the present invention may be had by referring to the following discussion and the accompanying drawings in which:

FIG. 1 is an elevational view of the exterior of a tank constructed in accordance with this invention;

FIG. 2 is a perspective view of a small area of the tanks shell, which illustrates the various planes and axes of curvature which are used to define the tanks shape;

FIG. 3 is a graphical representation of the tanks shape through a central vertical axis, which also shows the pressures which exist within the tank;

FIG. 4 is a graph which illustrates the interrelation between the volume of the tank and the values of A and H which are defined below in the specification;

FIG. 5 is the stress-elongation curve of one type of material which is suitable for construction of the present tank; and

FIG. 6 shows some typical shapes which tanks may assume in the practice of this invention.

It is known that a tank which has tensile forces in its walls which are equal at all portions of the shell must have a certain shape and contain fluids which have a particular density and pressure.

The ideal tank shape may be defined in different ways, but its most accurate definition lies in the formula which is referred to herein as the basic shape equation. The basic shape equation, which describes the conditions and shape of any incremental area on the shell is given as follows:

where F is the tensile force in the shell, expressed in force per linear unit;

r is the radius of curvature of the incremental area taken .in the meridian plane;

r is the radius of curvature of the incremental area taken in a plane perpendicular to the meridian plane; and

P is the pressure at the incremental area and is the product of the density (7) of the fluid and the theoretical pressure head (z) at the incremental area.

The quantities which appear in the basic shape equation will be understood by referring to the drawings. In FIG. 1, it will be noted that the tank is of a flattened spheroidal shape, having a substantially flat bottom surface which rests on the ground or other flat horizontal supporting surface. On occasions it will be desirable to incline the bottom portion in various manners for purposes of drainage or stability. The tank is symmetrical about the vertical axis AA which constitutes the axis of gyration of the curve of its cross-sectional shape. All planes passing through the axis of gyration AA are termed meridian planes.

P or purposes of illustration, an incremental area of the tank shell is designated 2 in FIGS. 1 and 2. Like all other incremental area-s of the shell, it is subjected to tensile forces P which are equal in all directions. The units of F will usually be in pounds per foot. A line normal to this incremental area is illustrated at BB in FIG. 2. Line B B lies in the meridian plane MP.

The incremental area 2 has a compound curvature which in the meridian plane MP has a radius of 1' with the center of curvature lying at c on the normal line BB.

Perpendicular to the meridian plane MP and including the normal line BB is a plane which has been designated PP, in which the radius of curvature is shown to be r The center of curvature in the plane PP is, of course, at the intersection of lines AA and BB. Except at the top and the bottom of the tank, r will always be greater than r A cross-sectional view of the tank, taken through a meredian plane, is shown in FIG. 3. Here, it will be seen that any tank conforming to the basic shape equation has a shape such that the greatest radius of curvature r in the meridian plane is at the top of the tank, and that the radius of curvature r for each incremental are becomes less progressively from the top toward the flat bottom of the tank.

In FIG. 3, the points designated 0 are the centers of curvature for their respective arcs which have been designated a. Thus, the topmost are a in the shell has a center c and the radius of curvature r in the meridian plane is the distance between c and a The remaining arcs a a a etc. have their centers of curvature at their respective points c c c etc. It is readily apparent that the radii of curvature diminish progressively as the arcs become closer to the flat bottom of the tank. The flat bottom 4 is, of course, transverse to the central vertical axis AA.

FIG. 3 also represents graphically the pressures which exist at the various levels of the tank. The pressure within the uppermost portion of the tank, i.e., at the are a is 'yH, where H is the theoretical pressure head which exists in this portion of the tank and 'y is the density of the fluid. Naturally, the pressure is greater at the lower portions of the tank. Numerically, it is equal to 'yz where z is the theoretical pressure head at the particular depth in the tank.

From the basic shape equation, it is apparent that tanks which meet its ideal conditions will have shapes and sizes which vary with the tensile forces existing in the shell, the density of the contained fluid and the pressure within the tank. FIG. 6 is demonstrative of some of the shapes which are arrived at by using the basic shape equation. The flattest profile 8 is one which may exist when a dense fluid fills the tank with a relatively low gas pressure superimposed thereon. If a lighter fluid is used, the internal pressure increased or the tension in the shell is raised, the shape may rise to look something like either of the profiles 10 or 12.

During the normal use of any tank, the depth of liquid and the tanks internal pressure will vary from time to time. When this occurs in a usual rigid spheroidal steel tank, the tensile forces in the shell will become quite unequal and may cause rupture of the shell in the absence of precautionary bracing. However, in the tank which constitutes the present invention, the walls are flexible and stretchable and thus will permit the shell to approach a spheroidal shape which will approximate the basic shape equation for the particular tank contents.

In a rigid tank, as the volume or the pressure at the top of the tank decreases the tensile forces in the shell at the top of the tank will be less than the tensile forces at the bottom of the tank. In the event of an increased pressure at the top of the tank, even combined with a lowering of the liquid level, the tensile forces in the Zone of the are a may become extremely great, to the extent that the tank will rupture if it is not provided with additional bracing.

In a like manner, the rigid tanks of the prior art may even be subjected to compressive forces in the shell which may cause a failure. This will happen when a tank is designed for use with .a gas or a liquid which has a low density, and it is filled with a more dense fluid. When this takes place, the shell at the zone around the arc will receive a compressive force which will cause buckling of the steel plates.

These above-mentioned contingencies are not present to any appreciable degree in the tanks which are made of a flexible and stretchable material. The flexibility of the material precludes rupture when the shell receives compressive forces, and the stretchability of the material prevents failure when excessive tensile forces are encountered.

Quite significantly, the stretcha bility of the shell material will permit the tank to change its shape so that it will more closely approach the shape described by the basic shape equation. This, in turn, will reduce the differences between the forces in the shell so that undue tensile stresses will be avoided. A more eificient use of the shell material is thus afforded if it possesses the characteristic of stretchability, and the need for additional bracing and reinforcement is eliminated.

The tank materials used in the present invention are also elastic. This makes it possible for them gradually to contract when fluids are drawn from the container, even when the shell material had been stressed beyond the linear portion of the stress-elongation curve. In so contracting, the shell will continue to assume a shape which resembles the basic shape equation, thus tending to keep the tensile forces equal at all portions of the shell. Sagging of the top of the tank is also averted in this manner.

Some of the other advantages of using a stretchable and flexible material are that the tank may be erected or dismantled in a relatively short time by an untrained crew of workmen. This eliminates the nee-d for experienced crews which presently are called upon to erect the steel speroidal tanks.

stretchable and flexible materials such as rubber or polyurethane sheeting possess the obvious advantage that they do not require a preservative or decorative coating such as paint, and maintenance costs are reduced accordingly.

Other less apparent advantages of this new tank construction are of major significance. Due to the stretchability of the tank walls, the tank may be initially constructed on a reduced scale. Once it is at the site, it may be stretched to the desired shape by filling it to the prescribed level with liquid, gas or both. The final volume will be at least 125% of its initial volume. Using this procedure, the tank may be fabricated in an area which is much smaller than would be necessary to form a tank .of full final size.

The stretchability of the tank walls is also important from a standpoint of safety. Once the volume of the tank contents exceed its designed volume, the walls of the tank simply distend further to enable it to hold the increased volume. Naturally, the tanks are designed with a safety factor so that considerable overfilling may take place without bursting of the tank. This feature of the invention is one which distinguishes it from those prior art devices made of flexible but unstretchable material, which cannot yield to any appreciable extent. Once their contents exceed 100% of design capacity, they will burst. Relief valves may prevent this contingency, but would result in the discharge of the fluid from the tank. This is not only wasteful, but, in the instance of inflammable fluids, may be quite hazardous.

Of course, the precise characteristics of the materials used for forming the improved tank are not critical and may vary from one installation to another. Consideration must be given to the chemical nature of the stored fluid, so that it will not act adversely on the material which forms the tank. Obviously, ordinary rubber is unsuitable for the storage of hydrocarbons, so some other material must be selected. Polyurethane sheeting is suitable since it is not harmfully affected by hydrocarbons.

\ In specifying the characteristics of the shell material, wide ranges have been selected which will satisfy the requirements of various sized tanks. The tensile strength must be at least 100 p.s.i., and the permissible elongation must be at least 100%. The stress-strain properties must be such that the permissible tensile stress without failure is at least twice the tensile stress at 50% elongation. These properties must exist throughout the temperature range to which a tank will be subjected.

The shell material must be flexible and stretchable to the extent that it will be capable of readily assuming the shape dictated by the tanks loaded condition. Also, it is desirable that the material be abrasion-resistant and capable of exposure to the sun and the atmosphere over ap preciable extents of time.

By way of example, the following properties are definitive of suitable polyurethane materials which are presently available:

(1) Tensile strength is 3000-8500 p.s.i.

(2) Elongation is 200800% without failure.

(3) Stress at 50% elongation is 500-800 p.s.i.

(4) Highly flexible.

(5) Good retention of physical characteristics throughout normal range of atmospheric temperatures.

(6) Resistant to abrasion, atmosphere and various fluids which may be stored in the tank.

Naturally, development of new materials with improved properties will aid those who practice this invention.

One important feature of the improved tanks which are described above is that they may be designed by using procedures which are far simpler than those which have been used in the prior art.

Previously, engineers who have designed spheroidal tanks have been unable to determine the final volume of a tank without first constructing the tank or a prototype thereof or by graphical or computational trial and error.

It has been discovered that the volume is interrelated to the parameters used in solving the basic shape equation. Specifically, one parameter is A, and its value is equal to the square root of F/v.

The other parameter used in solving the basic shape equation is H, which is the theoretical pressure head existing within the upper confines of the tank. This is shown in FIG. 3.

The relationship between these parameters and the tank volume is that the volume is directly proportional to A raised to the third power when the H /A ratio is held c0nstant. Based upon these relationships, the curve of FIG. 4 may be plotted by first finding the volume of only one tank with a given H /A ratio, and then projecting it using the newly-found interrelationship of these quantities. The curve of FIG. 4 is drawn on log-log paper.

In a graph such as the one shown in FIG. 4, an engineer may use the selected values of volume and H, to find the suitable value of A. The detailed use of the graph is de scribed below. The values of A are, of course, set up for the commercially available materials which may be used for tank construction.

Another mathematical relationship which aids the design engineer is that the shapes of tanks having a constant H/A ratio will be similar, although their volumes will differ as described above. This relationship comes into play in the design of stretchable tanks, where the fabricated tank is smaller than it will be when filled to its designed conditions. Once the engineer has determined the A of the filled tank (A and the elongation (e) of the shell material at the filled condition, he may easily determine the desired value of A when the tank is constructed (A And, since the H/A ratio is known and held constant, the value of H may be determined. Then, the A and 1-1 are used in a usual manner to plot the cross-sectional shape of the tank which is constructed.

Design procedures In designing a tank of the type contemplated by this inventionthe en ineer may select the desired final volume of the tank. He must decide the theoretical pressure head H, measured in linear units, which is to exist within the top of the tank when filled to its design capacity.

In selecting the theoretical pressure head H, the engineer must consider the type of conditions to which the tank will be exposed as, for example, the load which will be placed on top of the tank in the event of snow or increased gas pressures when the tank contents become heated. With increased value of H, the overall width of the tank will be reduced, so this may also be considered when the site is of a restricted size.

With the selected values of H and volume, a set of curves such as shown in FIG. 4 may be consulted to find the value of A. A is equal to so that once A and v (the density of the tank contents) are known, the engineer may compute the tensile forces 10 F which will exist in the filled tank. The tensile force F is, of course, the product of the stress (a) and the thickness (t) of the material. Thus, the required thickness of the tank walls may be ascertained by dividing the tensile force F by the maximum allowable force (c to which the shell material may be subjected. A normal safety factor will be used in setting the maximum allowable stress.

From the maximum allowable stress (c the engineer may refer to a stress-elongation curve such as the one shown in FIG. 5 to determine the extent of elongation (e) which will exist when the tank is filled. The value of elongation (e) is, as usual, the extent to which any portion of the shell is stretched beyond its initial unstressed length.

Knowing the extent of elongation in the filled tank, the initial A (A and the initial H (H may be computed, since it has been discovered that for a constant H /A ratio, the shape of the tank is similar for all sizes of the tank.

Thus

1 e where A is the A of the tank when filled to the design capacity.

1 1 i 2) P 72 may be solved using any known graphical or mathematical procedures. One solution of this equation, using H and A is described by Timoshenko and Woinowsky-Krieger in Section 108 of their book Theory of Plates and Shells, McGraw-Hill, 1959, which is incorporated herein by reference. In the notation used by Timoshenko et al., the symbol d is equivalent to H and a is used for A.

Applying this procedure to a specific example, assume that a tank is to be constructed of polyurethane which has an allowable stress (o' of 775 p.s.i. The tank is to contain 10,000 barrels of gasoline which has a density of 43.6 pounds per cubic foot. The desired pressure head within the top of the tank (H is 3 feet.

With this data, the chart or graph of FIG. 4 is consulted. From the known values of H and the volume, it will be seen that the value for A must be 12.6.

Knowing that A is 12.6 feet and that the maximum allowable stress of the material is 775 p.s.i., the engineer may use the formula to find the thickness as:

A (12.6) (43.6) 12.7, 12 775 The strain of the material of the filled tank is then read from the stress-elongation curve of FIG. for the maximum allowable stress (c of 775 psi. This value of elongation (e) is 200%.

8 Then the value of A for the unstressed vessel (A is found by computing And H is found by mences with the plotting or mathematical solution of the are a which has a radius (r equal to Using the shape defined by the basic shape equation, a form is prepared. The flexible, stretchable tank is built on the form and the form removed. Then the tank may be placed on the site and filled to its designed pressure and capacity which is at least 125% of its initial volume. Of course, any tank so constructed will have conventional fittings for filling, discharging and venting. These connections are known to those skilled in the art and are not described in detail in this specification.

The resulting tank will be ideally suited to the storage of large volumes of fluids, and it will possess all the advantages described hereinabove. The tensile forces in the shell will be equal or substantially so. It will change its shape as its conditions of loading vary, so that its shape will always approach the basic shape equation. Construction .and erection will be uncomplicated, and the expenses of maintenance will be minimal.

Only a preferred embodiment of the invention has been described as being illustrative of the invention. The types of materials used for the shell may vary widely, as will the nature of the enclosed fluids, either liquids or gases or both. On all occasions, the tank which is described in the following claims will be a significant and important departure from the prior art.

I claim:

1. A closed tank having walls made of a stretchable, flexible material which has a substantially uniform thickness and is capable of at least elongation without rupture, said tank having a shape of a solid of revolution about a central vertical axis, every central cross-section of which is an area bounded by a substantially linear bottom portion lying transversely to said central vertical axis and curved side and top portions, the arcs of which have different radii of curvature, the radii of curvature at successive points from the uppermost point of the tank toward said bottom portion being successively shorter.

2. The tank of claim 1 having a capacity in excess of 10,000 gallons.

3. The tank of claim 1 containing a volume of liquid and being inflated to at least of its initial volume.

4. The tank of claim 1 in which the shape of said area is defined by the formula where all symbols represent the quantities set forth in the specification.

5. The tank of claim 4 containing a volume of liquid and being inflated to at least 125% of its initial volume.

6. The tank of claim 4 wherein the radius of the uppermost are bounding said area is equal to where the symbols represent the quantities defined in the specification.

7. The tank of claim 6 containing a volume of liquid and being inflated to at least 125% of its initial volume.

8. The method of manufacturing a storage tank com prising the steps of (a) Fabricating a closed vessel of stretchable, flexible material having a shape defined by the equation where F and 'y are the constants and r 1' and z represent the quantities set forth in the specification; and

(b) filling said closed vessel to elongate its Walls and increase its volume to at least 125% of its initial volume.

9. The method of manufacturing a storage tank, comprising the steps of (a) Selecting (1) a volume of the contents within a completed tank; and (2) the theoretical pressure head which exists Within the top of said tank,

(b) Referring to a table with said volume and pressure, and determining therefrom a value of A which is a constant, the value of which is dependent upon 1) the forces per unit length in the wall of said tank and (2) the density of the tank contents,

(c) Computing the shape of a tank using said A and said theoretical pressure head, using as a basis the as defined in the specification,

(d) Fabricating a form in accordance with the shape of the tank derived from step (c) above;

(e) Building on said form a flexible and stretchable shell of substantially uniform thickness,

(f) Removing said shell from said form, and

(g) Filling said shell to said final tank volume.

10. The method according to claim 9 wherein said flexible shell is capable of sustaning 100% elongation without failure, said form is similar in shape to but smaller in size than the final volume of the tank, and the filling step causes an increase in volume of said tank.

References Cited by the Examiner UNITED STATES PATENTS 1,622,787 3/ 1927 Horton 220-1 2,119,518 6/ 1938 Boardrnan 2201 2,851,075 9/ 1958 Palfey l.5

FOREIGN PATENTS 1,231,391 11/1960 France.

1,292,370 3/1961 France.

FRANKLIN T. GARRETT, Primary Examiner. 

1. A CLOSED TANK HAVING WALLS MADE OF A STRETCHABLE, FLEXIBLE MATERIAL WHICH HAS A SUBSTANTIALLY UNIFORM THICKNESS AND IS CAPABLE OF AT LEAST 100% ELONGATION WITHOUT RUPTURE, SAID TANK HAVING A SHAPE OF A SOLID OF REVOLUTION ABOUT A CENTRAL VERTICAL AXIS, EVERY CENTRAL CROSS-SECTION OF WHICH IS AN AREA BOUNDED BY A SUBSTANTIALLY LINEAR BOTTOM PORTION LYING TRANSVERSELY TO SAID CENTRAL VERTICAL AXIS AND CURVED SIDE AND TOP PORTIONS, THE ARCS OF WHICH HAVE DIFFERENT RADII OF CURVATURE, THE RADII OF CURVATURE AT SUCCESSIVE POINTS FROM THE UPPERMOST POINT OF THE TANK TOWARD SAID BOTTOM PORTION BEING SUCCESSIVELY SHORTER. 